Lesson video

Hi, I'm Mr. Chan.

And in this lesson, we're going to look at expressing one number as a fraction or percentage of another number without a calculator.

Let's look at expressing one number as a fraction or percentage of another without a calculator.

Let's begin with writing five centimetres as a percentage of 25 centimetres.

So expressing this firstly, as a fraction, five centimetres as a fraction of 25 centimetres, we would write like this, 5/25.

And that's how we would write that as a fraction, but that's not quite a percentage yet.

Remember, percentages are out of 100.

So we need to create an equivalent fraction out of 100, and we can do that by multiplying the denominator by four and also the numerator by four to create an equivalent fraction out of 100.

Now we have 20/100, because it's already out of 100 now that would represent 20%.

In this example, we're asked to write three millimetres as a percentage of one centimetre.

You've got to be really careful with questions like this because the units don't actually match up.

Now, it doesn't really matter what unit you decide to choose to make them match but the important thing is that both units are the same.

So in this question, I'm going to change, or think about one centimetre as 10 millimetres.

So we know one centimetre equals 10 millimetres.

So we're now in a position to write that as a fraction, three millimetres as a percentage of 10 millimetres would be three-tenths, 3/10.

Again, to try and get this into a percentage, we need this to be out of 100.

So multiplying the denominator by 10 would get that to 100 and we must multiply the numerator by 10 also to create the equivalent fraction.

What we end up with is 30/100, which is 30%.

So three millimetres as a percentage of one centimetre is 30%.

Here are some questions for you to try, pause the video to complete the task.

Resume the video once you're finished.

Here are the answers to the first question.

We're asked to write the first quantity as a fraction and the percentage of the second quantity.

So let's look at part A.

17 metres out of 20 metres.

Well, I would have started off by writing the fraction 17/20.

And to get that to a percentage, I would have tried to get the fraction out of 100.

And in order to do that, I would multiply the denominator by five, to keep the fraction equivalent, I would have to multiply the numerator by five also, that gives me a fraction 85/100, so that means it's 85%.

In question 1E, 650 grammes out of one kilogramme.

Remember we have to keep the units the same, so in this example, in this question, I would have used grammes for both measurements, so I would have wrote 650/1000 to start with, and then try and find that as a percentage.

Here's a question for you to try.

Pause the video is complete the task, resume the video once you're finished.

Here are the answers for question two.

In part A, the question asks what fraction of money does Brett have left? So in order to work that out, you have to work out what fraction of the money he spent.

And subtract that.

So he actually spends 11 pounds out of the 20, so the fraction he has left is 9/20.

What percentage of that does he have left? So we're converting 9/20 into a percentage.

I would do that by multiplying the denominator by five and also the numerator by five to get 45/100, that tells me it's 45% that he has left.

In this example, we're asked to write 27 pounds as a percentage of 60 pounds.

So writing that as a fraction, we would write 27/60, so 27-sixtieths.

Now, in order to write this as a percentage without a calculator, we would have to try and get the fraction to be out of 100.

Now to get from sixtieths as a denominator to 100 is a little bit tricky.

So I'm going to think about creating a middle step here, and write the function out of twentieths first by dividing the denomination by three and also the numerator by three.

So 27/60 is equivalent to 9/20.

The reason why I did create the equivalent fraction out of twentieths, is because I can now multiply the denominator by five and also the numerator by five to get the fraction out of 100.

And once the fraction's out of 100, writing that as a percentage is pretty straightforward, that would represent 45%.

So now I know the answer 27 pounds as a percentage of 60 pounds is 45%.

Here's a question for you to try.

Pause the video to complete the task, resume the video once you're finished.

Here's the answer to question three.

So Tommy got 28 out of 40 in his geography test.

So I would write a fraction representing that 28/40.

And in order to create an equivalent fraction out of 100, you can see that I simplified the fraction 28/40 by dividing the denominator by two and also the numerator.

And once I got the 14/20, I multiplied the denominator and numerator by five to get the fraction out of 100, and that's quite easy to convert to a percentage.

So Tommy got 70% in his test.

Here's another question for you to try.

Pause the video to complete the task, resume the video once you're finished.

Here's the answer for question four.

So in this question we're comparing which bar of chocolate contains the high percentage of nuts, so we have to find out what percentage each bar contains to start with.

Setting those up as fractions as you can see, and then simplifying the fractions and what we're trying to aim for, remember, is trying to get the fraction out of 100 to create the percentage, and once we've found that we can say that Nutz has the higher percentage of nuts.

That's all for this lesson, thanks for watching.